An Ideal-Based Dot Total Graph of a Commutative Ring

In this paper, we introduce and investigate an ideal-based dot total graph of commutative ring R with nonzero unity. We show that this graph is connected and has a small diameter of at most two. Furthermore, its vertex set is divided into three disjoint subsets of R. After that, connectivity, clique...

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Bibliographic Details
Published inMathematics (Basel) Vol. 9; no. 23; p. 3072
Main Authors Ashraf, Mohammad, Asalool, Jaber H., Alanazi, Abdulaziz M., Alamer, Ahmed
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.12.2021
Subjects
commutative rings
Commutativity
Connectivity
dot total graph
ideal-based
Mathematics
Rings (mathematics)
Vertex sets
zero-divisor graph
zero-divisors
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Summary:In this paper, we introduce and investigate an ideal-based dot total graph of commutative ring R with nonzero unity. We show that this graph is connected and has a small diameter of at most two. Furthermore, its vertex set is divided into three disjoint subsets of R. After that, connectivity, clique number, and girth have also been studied. Finally, we determine the cases when it is Eulerian, Hamiltonian, and contains a Eulerian trail.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9233072